Best 1208 quotes in «math quotes» category

I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain ... But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty.

... I left Caen, where I was living, to go on a geological excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.

I'm really good with problems. I can solve a differential equation in my head. I chew through trig angles like candy. I know this, and it just makes it worse. Because I don't know how to solve this one.

Infinity exist unfortnately what will happen if we accept it?? After all numbers are taken what happens?? We will start with Omega+1 Then Omega+Omega+1... Think on this, this is the infinitive road, I gave it to you but what you will do?

Infinity...is used in physics simply as a shorthand for "a very big number.

[In high school] my interests outside my academic work were debating, tennis, and to a lesser extent, acting. I became intensely interested in astronomy and devoured the popular works of astronomers such as Sir Arthur Eddington and Sir James Jeans, from which I learnt that a knowledge of mathematics and physics was essential to the pursuit of astronomy. This increased my fondness for those subjects.

In geometry, whenever we had to find the area of a circle, pi * radius squared, I would get really hungry for pie. Square pie.

In my opinion, defining intelligence is much like defining beauty, and I don’t mean that it’s in the eye of the beholder. To illustrate, let’s say that you are the only beholder, and your word is final. Would you be able to choose the 1000 most beautiful women in the country? And if that sounds impossible, consider this: Say you’re now looking at your picks. Could you compare them to each other and say which one is more beautiful? For example, who is more beautiful— Katie Holmes or Angelina Jolie? How about Angelina Jolie or Catherine Zeta-Jones? I think intelligence is like this. So many factors are involved that attempts to measure it are useless. Not that IQ tests are useless. Far from it. Good tests work: They measure a variety of mental abilities, and the best tests do it well. But they don’t measure intelligence itself.

In mathematics, in physics, people are concerned with what you say, not with your certification. But in order to speak about social reality, you must have the proper credentials, particularly if you depart from the accepted framework of thinking. Generally speaking, it seems fair to say that the richer the intellectual substance of a field, the less there is a concern for credentials, and the greater is concern for content.

Réduites à des théories générales, les mathématiques seraient une belle forme sans contenu. Reduced to general theories, mathematics would be a beautiful form without content.

In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began.

INTROSPECTION AND INSANITY: A GODELIAN PROBLEM I think it can have suggestive value to translate Godel's Theorem into other domains, provided one specifies in advance that the translations are metaphorical and are not intended to be taken literally. That having been said, I see two major ways of using analogies to connect Godel's Theorem and human thoughts. One involves the problem of wondering about one's sanity. How can you figure out if you are sane? This is a Strange Loop indeed. Once you begin to question your own sanity, you can get trapped in an ever-tighter vortex of self-fulfilling prophecies, though the process is by no means inevitable. Everyone knows that the insane interpret the world via their own peculiarly consistent logic; how can you tell if your own logic is 'peculiar' or not, given that you have only your own logic to judge itself? I don't see any answer. I am just reminded of Godel's second Theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent...

I remember our childhood days when life was easy and math problems hard. Mom would help us with our homework and dad was not at home but at work. After our chores, we’d go to the old fort museum with clips in our hair and pure joy in our hearts. You, sister, wore the bangles that you, brother, got as a prize from the Dentist. “Why the bangles?” the Dentist asked, surprised, for boys picked the stickers of cars instead. “They’re for my sisters,” you said. Mom would treat us to a bottle of Coke, a few sips each. Then, we’d buy the sweet smelling bread from the same white van and hand-in-hand, we’d walk to our small flat above the restaurant. I remember our childhood days. Do you remember them too?

{Replying to G. H. Hardy's suggestion that the number of a taxi (1729) was 'dull', showing off his spontaneous mathematical genius} No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways, the two ways being 13 + 123 and 93 + 103.

I started studying law, but this I could stand just for one semester. I couldn't stand more. Then I studied languages and literature for two years. After two years I passed an examination with the result I have a teaching certificate for Latin and Hungarian for the lower classes of the gymnasium, for kids from 10 to 14. I never made use of this teaching certificate. And then I came to philosophy, physics, and mathematics. In fact, I came to mathematics indirectly. I was really more interested in physics and philosophy and thought about those. It is a little shortened but not quite wrong to say: I thought I am not good enough for physics and I am too good for philosophy. Mathematics is in between.

It baffled me how people could resist math's gorgeousness, but people did, and people do. The fine of its purity drives them away, the purity of the fine, unmixed with the heaviness of unnecessitated being.

I studied calculus for the first time, which to me was an amazingly empowering experience which I could really see how you could understand all sorts of things, and I decided that chemistry and biology just had too much memory for me to be interested. Physics was very easy.

... I succeeded at math, at least by the usual evaluation criteria: grades. Yet while I might have earned top marks in geometry and algebra, I was merely following memorized rules, plugging in numbers and dutifully crunching out answers by rote, with no real grasp of the significance of what I was doing or its usefulness in solving real-world problems. Worse, I knew the depth of my own ignorance, and I lived in fear that my lack of comprehension would be discovered and I would be exposed as an academic fraud -- psychologists call this "imposter syndrome".

. . . I still wouldn't be able to control myself around him, and I'm math geek enough to know that equation doesn't work out.

It is strange a difference comes from a subtraction.

[The Old Astronomer to His Pupil] Reach me down my Tycho Brahe, I would know him when we meet, When I share my later science, sitting humbly at his feet; He may know the law of all things, yet be ignorant of how We are working to completion, working on from then to now. Pray remember that I leave you all my theory complete, Lacking only certain data for your adding, as is meet, And remember men will scorn it, 'tis original and true, And the obloquy of newness may fall bitterly on you. But, my pupil, as my pupil you have learned the worth of scorn, You have laughed with me at pity, we have joyed to be forlorn, What for us are all distractions of men's fellowship and smiles; What for us the Goddess Pleasure with her meretricious smiles. You may tell that German College that their honor comes too late, But they must not waste repentance on the grizzly savant's fate. Though my soul may set in darkness, it will rise in perfect light; I have loved the stars too fondly to be fearful of the night. What, my boy, you are not weeping? You should save your eyes for sight; You will need them, mine observer, yet for many another night. I leave none but you, my pupil, unto whom my plans are known. You 'have none but me,' you murmur, and I 'leave you quite alone'? Well then, kiss me, -- since my mother left her blessing on my brow, There has been a something wanting in my nature until now; I can dimly comprehend it, -- that I might have been more kind, Might have cherished you more wisely, as the one I leave behind. I 'have never failed in kindness'? No, we lived too high for strife,-- Calmest coldness was the error which has crept into our life; But your spirit is untainted, I can dedicate you still To the service of our science: you will further it? you will! There are certain calculations I should like to make with you, To be sure that your deductions will be logical and true; And remember, 'Patience, Patience,' is the watchword of a sage, Not to-day nor yet to-morrow can complete a perfect age. I have sown, like Tycho Brahe, that a greater man may reap; But if none should do my reaping, 'twill disturb me in my sleep So be careful and be faithful, though, like me, you leave no name; See, my boy, that nothing turn you to the mere pursuit of fame. I must say Good-bye, my pupil, for I cannot longer speak; Draw the curtain back for Venus, ere my vision grows too weak: It is strange the pearly planet should look red as fiery Mars,-- God will mercifully guide me on my way amongst the stars.

I think scientists have a valid point when they bemoan the fact that it's socially acceptable in our culture to be utterly ignorant of math, whereas it is a shameful thing to be illiterate.

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.

It’s all accumulation and the aftermath,' she says as I would question her about the failing earth and giants unaware that they are sinking everyday

I've got a few ideas," (Amy) admitted. "But I don't know where we're going in the long term. I mean - have you ever thought about what this ultimate treasure could be?" "Something cool." (Dan) "Oh, that's real helpful. I mean, what could make somebody the most powerful Cahill in history? And why thirty-nine clues?" Dan shrugged. "Thirty-nine is a sweet number. It's thirteen times three. It's also the sum of five prime numbers in a row - 3,5,7,11,13. And if you add the first three powers of three, 3 to the first, 3 to the second, and s to the third, you get thirty-nine." Amy stared at him. "How did you know that?" "What do you mean? It's obvious.

I will never listen to ocean waves or view a beautiful sunset in quite the same way again. That is perhaps the greatest gift one can gain by delving into calculus: It is a whole new way of looking at the world, accessible only through the realm of mathematics.

I've sort of been slacking off in my voodoo studies.I've trigonometry, you know?

Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power.

Man had been given a brain that could think in numbers, and it could not be coincidence that the world was unlocked by that very tool. To understand any aspect of the cosmos was to look on the face of God: not directly, but by a species of triangulation, because to think mathematically was to feel the action of God in oneself.

Luck is not some esoteric, godlike phenomenon. Luck is countable but undefinable. Luck easily can be explained as number of factors acting in a favour of a person. These factors' behaviour could be statistically proved , and the probability of such result is possible. It is not related to something explainable event. Actually, the miracle would be if these events (luck) are not in presence in our life. The matter as then would be mathematics proved wrong. So, make your luck!"

Logic, it is often said, is the study of valid arguments. It is a systematic attempt to distinguish valid arguments from invalid arguments.

Math test tomorrow. Check. Complete lack of preparation for test. Check.

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.

Mathematics had never had more than a secondary interest for him [her husband, George Boole]; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to give rest had no tendency to prove them.

Mathematics is not just a subject of education system, it is the soul of education system.

Math is made for idiots, here is what is the proccess in math class. The teacher show you few exercises, show you the formula, show you the way, say everything about the exercises and then she tell you to solve problems. So as for me the proccess is REPEAT!

Mathematics is one of the major modern mysteries. Perhaps it is the leading one, occupying a place in our society similar to the religious mysteries of another age. If we want to know something about what our age is all about, we should have some understanding of what mathematics is, and of how the mathematician operates and thinks.

Math anxiety is worst than a regular check up at the dentist.

Math is my Passion. Engineering is my Profession.

Math teaches us chaos or order, for god sake?

Math is a Chaos and it doesn't have order <--- what's the purpose of it?

Monty Jones: Dad, is there a word to describe answers that are completely correct but entirely useless under the circumstances? Professor Jones: Yes, yes there is.

Music was not so very different from mathematics. It was all just patterns and sequences. The only difference was that they hung in the air instead of on a piece of paper. Dancing was a grand equation. One side was sound, the other movement. The dancer's job was to make them equal.

Music is the melody that longs to be heard by someone who can appreciate it.

Music is a mixed mathematical science that concerns the origens, attributes, and distinctions of sound, out of which a cultivated and lovely melody and harmony are made, so that God is honored and praised but mankind is moved to devotion, virtue, joy, and sorrow.

My sub doesn't pay for me,” he says, pulling me to my feet. “That just doesn't happen.” “But we ordered so much,” I say helplessly. “It made you happy,” he says simply. “Now I get to play with you. And that makes me happy.” “I don't think it's that simple an equation.” “Maybe not,” he concedes. “But then, if if sex were the same thing as math, a lot more people would be lining up to take calculus.

No one shall expel us from the paradise which Cantor has created for us. {Expressing the importance of Georg Cantor's set theory in the development of mathematics.}

Naomi doubted that any human being really understood math, they simply all pretended to have it down pat, when in truth they were every bit as confused by it as she was. Math was nothing but a giant hoax, and everyone participated in it, everyone faked belief in math so they could be done with hideous classes and the drudgery of the hateful homework and get on with life. The sun came up every morning, so the sun was real, and every time you inhaled you got the air you needed, so the atmosphere was obviously real, but half the time when you tried to use math to solve the simplest problem, the math absolutely would not work, which meant that it couldn't be real like the sun and the atmosphere. Math was a waste of time.

Numbers never lie, after all: they simply tell different stories depending on the math of the tellers.

Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it opens to us a thousand different ways on which we can embark in all confidence; we are assured of meeting there no obstacles; but of all these ways, which will lead us most promptly to our goal? Who shall tell us which to choose? We need a faculty which makes us see the end from afar, and intuition is this faculty. It is necessary to the explorer for choosing his route; it is not less so to the one following his trail who wants to know why he chose it.